document.write( "Question 429551: Please help!
\n" ); document.write( "Can you include how you came to the answer as well, so I know how to do it myself in the future. Thanks so much!
\n" ); document.write( "Identify the type of equation presented in x^2+y^2-4x+12y-6=0 \n" ); document.write( "

Algebra.Com's Answer #298339 by Gersid(33) $\"\"$ $\"About$

You can put this solution on YOUR website!
Since the equation includes both an $\"x%5E2\"$ term and a $\"y%5E2\"$ term, it looks like it would be the equation of a conic section.
\n" ); document.write( " $\"x%5E2%2By%5E2-4x%2B12y-6+=+0\"$ Start by grouping the x- and y-terms.
\n" ); document.write( " $\"%28x%5E2-4x%29%2B%28y%5E2%2B12y%29-6+=+0\"$ Next add 6 to both sides.
\n" ); document.write( " $\"%28x%5E2-4x%29%2B%28y%5E2%2B12y%29+=+6\"$ Now complete the square in both x and y.
\n" ); document.write( " $\"%28x%5E2-4x%2B4%29%2B%28y%5E2%2B12y%2B36%29+=+6%2B4%2B36\"$ Simplify.
\n" ); document.write( " $\"%28x-2%29%5E2%2B%28y%2B6%29%5E2+=+46\"$ Compare this with the general form of the equation of a circle with center at (h, k) and radius r.
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2\"$
\n" ); document.write( "So what you have is the equation of a circle with its center at (2, -6) and a radius $\"r+=+sqrt%2846%29\"$ . \n" ); document.write( "

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